Question

this square has an area of 13 square units. what is the side length of this square? it does not equal a whole number, so lets estimate its value. between which two whole numbers is the side length, $sqrt{13}$ units? $sqrt{13}$ units is between the whole numbers. 1 and 2 2 and 3 3 and 4 4 and 5 5 and 6

Explanation:

Step1: Recall square - area formula

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 13$, then $s=\sqrt{13}$.

Step2: Find the range of $\sqrt{13}$

We know that $3^{2}=9$ and $4^{2}=16$. Since $9<13<16$, we have $\sqrt{9}<\sqrt{13}<\sqrt{16}$, which simplifies to $3 < \sqrt{13}<4$.

Answer:

3 and 4